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Question
if `sec theta = 5/4` find the value of `(sin theta - 2 cos theta)/(tan theta - cot theta)`
Solution
We have `sec theta= 5/4`
In ΔABC
`AC^2 = AB^2 + BC^2`
`=> (5)^2 = AB^2 + (4)^2`
`=> AB^2 = 25 - 16`
=> AB = 3
`∴ sin theta (AB)/(AC) = 3/5 , cos theta = 4/5, tan theta =3/4 , cot theta = 3/4`
NOw
`(sin theta - 2 cos theta)/(tan theta - cot theta) = (3/5 - 2 xx 4/5)/(3/4 - 4/3)`
`= 1/5 xx (3-8)/((9 - 16)/12)`
`= 1/5 xx (-5/7)xx12`
`= 12/7`
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